B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

23
B-Tree Insert and Delete Demo

Transcript of B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Page 1: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

B-Tree Insert and Delete Demo

Page 2: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Demo• Demo slide by: Dr. J. Johnson

Page 3: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

• Suppose we start with an empty B-tree and keys arrive in the following order:1 12 8 2 25 6 14 28 17 7 52 16 48 68 3 26 29 53 55 45

• We want to construct a B-tree of order 5• The first four items go into the root:

• To put the fifth item in the root would violate condition 4• Therefore, when 25 arrives, pick the middle key to make a

new root

Constructing a B-tree

1281 2

Page 4: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Constructing a B-treeAdd 25 to the tree

1 12 8 2 25 6 14 28 17 7 52 16 48 68 3 26 29 53 55 45

1281 2 25

Exceeds Order. Promote middle and split.

Page 5: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Constructing a B-tree (contd.)

6, 14, 28 get added to the leaf nodes:

1 12 8 2 25 6 14 28 17 7 52 16 48 68 3 26 29 53 55 45

12

8

1 2 25

12

8

1 2 2561 2 2814

Page 6: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Constructing a B-tree (contd.)

Adding 17 to the right leaf node would over-fill it, so we take the middle key, promote it (to the root) and split the leaf

1 12 8 2 25 6 14 28 17 7 52 16 48 68 3 26 29 53 55 45

1 12 8 2 25 6 14 28 17 7 52 16 48 68 3 26 29 53 55 45

12

8

2 2561 2 2814 2817

Page 7: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Constructing a B-tree (contd.)7, 52, 16, 48 get added to the leaf nodes

1 12 8 2 25 6 14 28 17 7 52 16 48 68 3 26 29 53 55 45

12

8

2561 2 2814

17

7 5216 48

Page 8: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Constructing a B-tree (contd.)

Adding 68 causes us to split the right most leaf, promoting 48 to the root

1 12 8 2 25 6 14 28 17 7 52 16 48 68 3 26 29 53 55 45

8 17

7621 161412 52482825 68

Page 9: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Constructing a B-tree (contd.)

Adding 3 causes us to split the left most leaf

1 12 8 2 25 6 14 28 17 7 52 16 48 68 3 26 29 53 55 45

48178

7621 161412 25 28 52 683 7

Page 10: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Constructing a B-tree (contd.)1 12 8 2 25 6 14 28 17 7 52 16 48 68 3 26 29 53 55 45

Add 26, 29, 53, 55 then go into the leaves

481783

1 2 6 7 52 6825 28161412 26 29 53 55

Page 11: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Constructing a B-tree (contd.)

Add 45 increases the trees level

1 12 8 2 25 6 14 28 17 7 52 16 48 68 3 26 29 53 55 45

481783

29282625 685553521614126 71 2 45

Exceeds Order. Promote middle and split.

Exceeds Order. Promote middle and split.

Page 12: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Exercise in Inserting a B-Tree

• Insert the following keys to a 5-way B-tree:• 3, 7, 9, 23, 45, 1, 5, 14, 25, 24, 13, 11, 8, 19, 4,

31, 35, 56

Page 13: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Answer to Exercise

Java Applet Source

Page 14: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Delete from a B-tree

• During insertion, the key always goes into a leaf. For deletion we wish to remove from a leaf. There are three possible ways we can do this:

• 1 - If the key is already in a leaf node, and removing it doesn’t cause that leaf node to have too few keys, then simply remove the key to be deleted.

• 2 - If the key is not in a leaf then it is guaranteed (by the nature of a B-tree) that its predecessor or successor will be in a leaf -- in this case can we delete the key and promote the predecessor or successor key to the non-leaf deleted key’s position.

Page 15: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Removal from a B-tree (2)

• If (1) or (2) lead to a leaf node containing less than the minimum number of keys then we have to look at the siblings immediately adjacent to the leaf in question: – 3: if one of them has more than the min’ number of keys then

we can promote one of its keys to the parent and take the parent key into our lacking leaf

– 4: if neither of them has more than the min’ number of keys then the lacking leaf and one of its neighbours can be combined with their shared parent (the opposite of promoting a key) and the new leaf will have the correct number of keys; if this step leave the parent with too few keys then we repeat the process up to the root itself, if required

Page 16: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Type #1: Simple leaf deletion

12 29 52

2 7 9 15 22 56 69 7231 43

Delete 2: Since there are enoughkeys in the node, just delete it

Assuming a 5-wayB-Tree, as before...

Note when printed: this slide is animated

Page 17: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Type #2: Simple non-leaf deletion

12 29 52

7 9 15 22 56 69 7231 43

Delete 52

Borrow the predecessoror (in this case) successor

56

Note when printed: this slide is animated

Page 18: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Type #4: Too few keys in node and its siblings

12 29 56

7 9 15 22 69 7231 43

Delete 72Too few keys!

Join back together

Note when printed: this slide is animated

Page 19: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Type #4: Too few keys in node and its siblings

12 29

7 9 15 22 695631 43

Note when printed: this slide is animated

Page 20: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Type #3: Enough siblings

12 29

7 9 15 22 695631 43

Delete 22

Demote root key andpromote leaf key

Note when printed: this slide is animated

Page 21: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Type #3: Enough siblings

12

297 9 15

31

695643

Note when printed: this slide is animated

Page 22: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Exercise in Removal from a B-Tree

• Given 5-way B-tree created by these data (last exercise):

• 3, 7, 9, 23, 45, 1, 5, 14, 25, 24, 13, 11, 8, 19, 4, 31, 35, 56

• Add these further keys: 2, 6,12

• Delete these keys: 4, 5, 7, 3, 14

Page 23: B-Tree Insert and Delete Demo. Demo Demo slide by: Dr. J. Johnson.

Answer to Exercise

Java Applet Source